The next step in cancer treatment is cancer immunotherapy, which seeks to fine tune our own immune responses against cancer through careful modulation of anti-tumor T cell responses as opposed to directly attacking cancer cells with harmful treatments such as radiation or chemotherapy. Effectively manipulating T cell responses against cancer without causing adverse effects requires striking a delicate balance between positive and negative T cell stimulation signals, essentially the gas and brakes of T cell responses. These stimulation signals are received by the T cell and transmitted through an intricate web of signaling pathways before ultimately being translated into a response, which may be to either attack or retreat. Achieving a quantitative understanding of how intracellular signaling processes determine the outcome of T cell encounters with cancer cells, which deliver both positive and negative stimulation signals, is a critical step in the drug design process. The goal of this proposal is to use mathematical modeling to determine the mathematical rules governing T cell responses to different stimulation signals. In general, insights gained during thi research may lead to a deeper understanding of the signaling mechanisms underlying T cell responses. Specifically, the quantitative relationships between upstream stimulation signals and downstream responses uncovered by this work may suggest clinically relevant, testable hypotheses such as predictions of which T cell receptor-targeting drugs and drug combinations may be more effective than others at eliminating cancer.